Subgroups — C₂²×D₃×C₄⋊(C₃⋊D₃) #13181599

Order 1728.

9116 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₃×C₃⋊D₃	C₂	1	2	yes	maximal, complemented
2	C₂²×C₄⋊(C₃⋊(C₃⋊D₃))	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×C₄⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₃²×C₄×D₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#6292	C₂	1	2	yes	maximal, complemented
6	C₂×D₃×C₄⋊(C₃⋊D₃)	C₂	1	24	yes	maximal, direct product factor
7	C₂³×C₄⋊(C₃⋊D₃)	—	3	1	no	maximal
8	C₂²×D₃×D₁₂	—	3	4	no	maximal
9	C₂³×C₃⋊(C₃⋊D₃)	C₂²	1	2	yes	complemented
10	C₂³×C₃×C₃⋊D₃	C₂²	1	2	yes	complemented
11	C₂³×C₃²×D₃	C₂²	1	1	yes	characteristic
12	C₂²×D₃×C₃⋊D₃	—	2	16	no	—
13	C₂²×D₃×C₃⋊D₃	C₂²	1	24	yes	complemented
14	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic, complemented
15	C₂×C₄⋊(C₃⋊(C₃⋊D₃))	C₂²	1	12	yes	complemented
16	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	12	yes	complemented
17	C₂²×C₃²×Dic₃	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₃²×C₄×D₃	C₂²	1	12	yes	complemented
19	C₂×#6292	C₂²	1	24	yes	complemented
20	D₃×C₄⋊(C₃⋊D₃)	C₂²	1	64	yes	direct product factor
21	C₂⁴×C₃⋊D₃	—	3	2	no	—
22	C₂³×D₃²	—	3	8	no	—
23	C₂³×C₃²×C₄	—	3	1	no	—
24	C₂²×C₄⋊(C₃⋊D₃)	—	3	1	no	—
25	C₂²×C₄⋊(C₃⋊D₃)	—	3	24	no	—
26	C₂²×C₄⋊(C₃⋊D₃)	—	3	4	no	—
27	C₂²×C₄⋊(C₃⋊D₃)	—	3	2	no	—
28	C₂²×C₄⋊(C₃⋊D₃)	—	6	4	no	—
29	C₂²×C₄⋊(C₃⋊D₃)	D₃	1	1	yes	characteristic, direct product factor
30	C₂²×C₃×D₁₂	—	3	4	no	—
31	C₂²×C₃×C₄×D₃	D₃	1	4	yes	complemented
32	C₂²×#626	—	3	8	no	—
33	C₂×D₃×D₁₂	—	3	96	no	—
34	C₂³×C₃³	C₂³	1	1	yes	characteristic
35	C₂²×C₃⋊(C₃⋊D₃)	—	2	8	no	—
36	C₂²×C₃⋊(C₃⋊D₃)	C₂³	1	12	yes	complemented
37	C₂²×C₃×C₃⋊D₃	—	2	8	no	—
38	C₂²×C₃×C₃⋊D₃	C₂³	1	12	yes	complemented
39	C₂²×C₃²×D₃	D₄	1	8	yes	complemented
40	C₂²×C₃²×D₃	C₂³	1	6	yes	—
41	C₂×D₃×C₃⋊D₃	—	2	96	no	—
42	C₂×D₃×C₃⋊D₃	C₂³	1	32	yes	complemented
43	C₂×C₃³×C₄	C₂³	1	6	yes	complemented
44	C₄⋊(C₃⋊(C₃⋊D₃))	C₂³	1	16	yes	complemented
45	C₃×C₄⋊(C₃⋊D₃)	C₂³	1	16	yes	complemented
46	C₂×C₃²×Dic₃	C₂³	1	6	yes	complemented
47	C₃²×C₄×D₃	C₂³	1	16	yes	complemented
48	#6292	C₂³	1	32	yes	complemented
49	C₂²×D₃×D₄	—	9	1	no	—
50	C₂³×D₁₂	—	9	4	no	—
51	C₂⁴×C₃²	—	3	1	no	—
52	C₂³×C₃⋊D₃	—	3	2	no	—
53	C₂³×C₃⋊D₃	—	3	8	no	—
54	C₂³×C₃⋊D₃	—	3	24	no	—
55	C₂³×C₃⋊D₃	—	6	16	no	—
56	C₂³×C₃⋊D₃	—	6	8	no	—
57	C₂³×C₃⋊D₃	C₂×D₃	1	2	yes	complemented
58	C₂³×C₃×D₃	—	3	8	no	—
59	C₂³×C₃×D₃	C₂×D₃	1	4	yes	—
60	C₂²×D₃²	—	3	96	no	—
61	C₂²×D₃²	—	6	64	no	—
62	C₂²×C₃²×C₄	—	2	4	no	—
63	C₂²×C₃²×C₄	—	3	1	no	—
64	C₂²×C₃²×C₄	—	3	12	no	—
65	C₂²×C₃²×C₄	C₂×D₃	1	4	yes	complemented
66	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic, complemented
67	C₂×C₄⋊(C₃⋊D₃)	—	3	24	no	—
68	C₂×C₄⋊(C₃⋊D₃)	—	3	12	no	—
69	C₂×C₄⋊(C₃⋊D₃)	—	3	48	no	—
70	C₂×C₄⋊(C₃⋊D₃)	—	3	64	no	—
71	C₂×C₄⋊(C₃⋊D₃)	—	6	48	no	—
72	C₂×C₄⋊(C₃⋊D₃)	C₂×D₃	1	12	yes	direct product factor
73	C₂²×C₃×Dic₃	C₂×D₃	1	4	yes	complemented
74	C₂×C₃×D₁₂	—	3	48	no	—
75	C₂×C₃×C₄×D₃	C₂×D₃	1	48	yes	complemented
76	C₂×#626	—	3	96	no	—
77	D₃×D₁₂	—	3	256	no	—
78	C₂²×C₃³	C₂×D₄	1	4	yes	complemented
79	C₂²×C₃³	C₂⁴	1	3	yes	—
80	C₂×C₃⋊(C₃⋊D₃)	—	2	24	no	—
81	C₂×C₃⋊(C₃⋊D₃)	C₂⁴	1	8	yes	complemented
82	C₂×C₃×C₃⋊D₃	—	2	24	no	—
83	C₂×C₃×C₃⋊D₃	C₂⁴	1	8	yes	complemented
84	C₂×C₃²×D₃	C₂×D₄	1	24	yes	complemented
85	C₂×C₃²×D₃	C₂⁴	1	4	yes	—
86	D₃×C₃⋊D₃	—	2	64	no	—
87	C₃³×C₄	C₂⁴	1	4	yes	complemented
88	C₃²×Dic₃	C₂⁴	1	4	yes	complemented
89	C₂⁴×D₃	—	9	8	no	—
90	C₂⁴×D₃	—	9	2	no	—
91	C₂²×C₃×D₄	—	9	1	no	—
92	C₂³×C₃×C₄	—	3	4	no	—
93	C₂²×#67	—	9	2	no	—
94	C₂×D₃×D₄	—	9	24	no	—
95	C₂²×D₁₂	—	3	4	no	—
96	C₂²×D₁₂	—	9	96	no	—
97	C₂²×D₁₂	—	9	8	no	—
98	C₂²×D₁₂	—	9	4	no	—
99	C₂²×D₁₂	—	9	1	no	—
100	C₂²×D₁₂	—	18	4	no	—
101	C₂²×C₄×D₃	C₃⋊D₃	1	1	yes	characteristic, complemented
102	C₂³×C₃²	—	2	4	no	—
103	C₂³×C₃²	—	3	8	no	—
104	C₂³×C₃²	—	3	6	no	—
105	C₂³×C₃²	C₂²×D₃	1	4	yes	—
106	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
107	C₂²×C₃⋊D₃	—	2	8	no	—
108	C₂²×C₃⋊D₃	—	3	12	no	—
109	C₂²×C₃⋊D₃	—	3	32	no	—
110	C₂²×C₃⋊D₃	—	3	48	no	—
111	C₂²×C₃⋊D₃	—	6	48	no	—
112	C₂²×C₃⋊D₃	—	6	96	no	—
113	C₂²×C₃⋊D₃	—	6	8	no	—
114	C₂²×C₃⋊D₃	—	6	32	no	—
115	C₂²×C₃⋊D₃	—	12	32	no	—
116	C₂²×C₃⋊D₃	C₂²×D₃	1	12	yes	complemented
117	C₂²×C₃×D₃	—	3	48	no	—
118	C₂²×C₃×D₃	—	6	32	no	—
119	C₂²×C₃×D₃	D₁₂	1	32	yes	complemented
120	C₂²×C₃×D₃	C₂²×D₃	1	24	yes	—
121	C₂×D₃²	—	3	128	no	—
122	C₂×D₃²	—	6	384	no	—
123	C₂×C₃²×C₄	—	2	24	no	—
124	C₂×C₃²×C₄	—	3	6	no	—
125	C₂×C₃²×C₄	—	3	16	no	—
126	C₂×C₃²×C₄	C₂²×D₃	1	24	yes	complemented
127	C₂×C₃²×C₄	C₂²×D₃	1	6	yes	complemented
128	C₄⋊(C₃⋊D₃)	—	3	32	no	—
129	C₄⋊(C₃⋊D₃)	—	3	16	no	—
130	C₄⋊(C₃⋊D₃)	—	3	64	no	—
131	C₄⋊(C₃⋊D₃)	—	6	64	no	—
132	C₄⋊(C₃⋊D₃)	C₂²×D₃	1	16	yes	direct product factor
133	C₂×C₃×Dic₃	C₂²×D₃	1	24	yes	complemented
134	C₃×D₁₂	—	3	64	no	—
135	C₃×C₄×D₃	C₂²×D₃	1	64	yes	complemented
136	#626	—	3	128	no	—
137	C₂³×D₄	—	27	1	no	Sylow
138	C₂×C₃³	C₂²×D₄	1	6	yes	complemented
139	C₂×C₃³	C₂⁵	1	1	yes	characteristic
140	C₃⋊(C₃⋊D₃)	—	2	8	no	—
141	C₃×C₃⋊D₃	—	2	8	no	—
142	C₃²×D₃	C₂²×D₄	1	8	yes	complemented
143	C₂⁴×C₃	—	3	4	no	—
144	C₂⁴×C₃	—	9	2	no	—
145	C₂³×D₃	—	3	8	no	—
146	C₂³×D₃	—	9	96	no	—
147	C₂³×D₃	—	9	8	no	—
148	C₂³×D₃	—	9	2	no	—
149	C₂³×D₃	—	9	24	no	—
150	C₂³×D₃	—	18	8	no	—
151	C₂³×D₃	—	18	64	no	—
152	C₂³×D₃	—	18	16	no	—
153	C₂³×D₃	C₂×C₃⋊D₃	1	1	yes	characteristic
154	C₂×C₃×D₄	—	9	12	no	—
155	C₂²×C₃×C₄	—	2	4	no	—
156	C₂²×C₃×C₄	—	3	4	no	—
157	C₂²×C₃×C₄	—	3	48	no	—
158	C₂²×C₃×C₄	D₃²	1	4	yes	complemented
159	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
160	C₂×#67	—	9	24	no	—
161	C₂²×Dic₃	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
162	D₃×D₄	—	9	64	no	—
163	C₂×D₁₂	—	3	48	no	—
164	C₂×D₁₂	—	9	256	no	—
165	C₂×D₁₂	—	9	96	no	—
166	C₂×D₁₂	—	9	48	no	—
167	C₂×D₁₂	—	9	12	no	—
168	C₂×D₁₂	—	18	48	no	—
169	C₂×C₄×D₃	C₂×C₃⋊D₃	1	12	yes	complemented
170	C₂²×C₃²	—	2	12	no	—
171	C₂²×C₃²	—	2	16	no	—
172	C₂²×C₃²	—	3	24	no	—
173	C₂²×C₃²	—	3	4	no	—
174	C₂²×C₃²	C₂×D₁₂	1	16	yes	complemented
175	C₂²×C₃²	D₃×D₄	1	4	yes	complemented
176	C₂²×C₃²	C₂³×D₃	1	12	yes	—
177	C₂²×C₃²	C₂³×D₃	1	3	yes	—
178	C₂×C₃⋊D₃	—	2	24	no	—
179	C₂×C₃⋊D₃	—	3	8	no	—
180	C₂×C₃⋊D₃	—	3	32	no	—
181	C₂×C₃⋊D₃	—	6	32	no	—
182	C₂×C₃⋊D₃	—	6	64	no	—
183	C₂×C₃⋊D₃	—	6	24	no	—
184	C₂×C₃⋊D₃	—	6	96	no	—
185	C₂×C₃⋊D₃	—	12	96	no	—
186	C₂×C₃⋊D₃	C₂³×D₃	1	8	yes	complemented
187	C₂×C₃×D₃	—	3	32	no	—
188	C₂×C₃×D₃	—	6	96	no	—
189	C₂×C₃×D₃	C₂×D₁₂	1	96	yes	complemented
190	C₂×C₃×D₃	C₂³×D₃	1	16	yes	—
191	D₃²	—	6	256	no	—
192	C₃²×C₄	—	2	16	no	—
193	C₃²×C₄	—	3	4	no	—
194	C₃²×C₄	C₂³×D₃	1	16	yes	complemented
195	C₃²×C₄	C₂³×D₃	1	4	yes	complemented
196	C₃×Dic₃	C₂³×D₃	1	16	yes	complemented
197	C₂⁵	—	27	2	no	—
198	C₂²×D₄	—	9	1	no	—
199	C₂²×D₄	—	27	24	no	—
200	C₂²×D₄	—	27	2	no	—
201	C₂²×D₄	—	27	1	no	—
202	C₂³×C₄	—	3	1	no	—
203	C₃³	C₂³×D₄	1	1	yes	characteristic, complemented, Sylow
204	C₂³×C₃	—	2	4	no	—
205	C₂³×C₃	—	3	24	no	—
206	C₂³×C₃	—	3	32	no	—
207	C₂³×C₃	—	9	12	no	—
208	C₂³×C₃	—	18	8	no	—
209	C₂³×C₃	C₂×D₃²	1	4	yes	—
210	C₂³×C₃	C₂²×C₃⋊D₃	1	1	yes	characteristic
211	C₂²×D₃	—	3	48	no	—
212	C₂²×D₃	—	6	32	no	—
213	C₂²×D₃	—	9	128	no	—
214	C₂²×D₃	—	9	48	no	—
215	C₂²×D₃	—	9	12	no	—
216	C₂²×D₃	—	9	32	no	—
217	C₂²×D₃	—	18	48	no	—
218	C₂²×D₃	—	18	384	no	—
219	C₂²×D₃	—	18	32	no	—
220	C₂²×D₃	—	18	8	no	—
221	C₂²×D₃	—	18	96	no	—
222	C₂²×D₃	—	36	32	no	—
223	C₂²×D₃	C₄⋊(C₃⋊D₃)	1	8	yes	direct product factor
224	C₂²×D₃	C₂²×C₃⋊D₃	1	6	yes	—
225	C₃×D₄	—	9	16	no	—
226	C₂×C₃×C₄	—	2	24	no	—
227	C₂×C₃×C₄	—	3	24	no	—
228	C₂×C₃×C₄	—	3	64	no	—
229	C₂×C₃×C₄	C₂×D₃²	1	24	yes	complemented
230	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	6	yes	complemented
231	#67	—	9	32	no	—
232	C₂×Dic₃	C₂²×C₃⋊D₃	1	6	yes	complemented
233	D₁₂	—	3	64	no	—
234	D₁₂	—	9	128	no	—
235	D₁₂	—	9	64	no	—
236	D₁₂	—	9	16	no	—
237	D₁₂	—	18	64	no	—
238	C₄×D₃	C₂²×C₃⋊D₃	1	16	yes	complemented
239	C₂×C₃²	—	2	24	no	—
240	C₂×C₃²	—	2	4	no	—
241	C₂×C₃²	—	3	8	no	—
242	C₂×C₃²	C₂²×D₁₂	1	24	yes	complemented
243	C₂×C₃²	C₂×D₃×D₄	1	6	yes	complemented
244	C₂×C₃²	C₂⁴×D₃	1	4	yes	—
245	C₂×C₃²	C₂⁴×D₃	1	1	yes	characteristic
246	C₃⋊D₃	—	2	8	no	—
247	C₃⋊D₃	—	6	8	no	—
248	C₃⋊D₃	—	6	32	no	—
249	C₃⋊D₃	—	12	32	no	—
250	C₃×D₃	—	6	32	no	—
251	C₃×D₃	C₂²×D₁₂	1	32	yes	complemented
252	C₂⁴	—	3	1	no	—
253	C₂⁴	—	9	2	no	—
254	C₂⁴	—	27	24	no	—
255	C₂⁴	—	27	2	no	—
256	C₂⁴	—	54	16	no	—
257	C₂×D₄	—	9	12	no	—
258	C₂×D₄	—	27	64	no	—
259	C₂×D₄	—	27	24	no	—
260	C₂×D₄	—	27	12	no	—
261	C₂²×C₄	—	3	1	no	—
262	C₂²×C₄	—	3	12	no	—
263	C₂²×C₄	D₃×C₃⋊D₃	1	1	yes	characteristic, complemented
264	C₂²×C₃	—	2	12	no	—
265	C₂²×C₃	—	2	16	no	—
266	C₂²×C₃	—	3	96	no	—
267	C₂²×C₃	—	3	16	no	—
268	C₂²×C₃	—	9	8	no	—
269	C₂²×C₃	—	18	24	no	—
270	C₂²×C₃	D₃×D₁₂	1	16	yes	complemented
271	C₂²×C₃	C₂×C₄⋊(C₃⋊D₃)	1	4	yes	complemented
272	C₂²×C₃	C₂²×D₃²	1	12	yes	—
273	C₂²×C₃	C₂³×C₃⋊D₃	1	3	yes	—
274	C₂×D₃	—	3	32	no	—
275	C₂×D₃	—	6	96	no	—
276	C₂×D₃	—	9	32	no	—
277	C₂×D₃	—	9	8	no	—
278	C₂×D₃	—	18	32	no	—
279	C₂×D₃	—	18	256	no	—
280	C₂×D₃	—	18	96	no	—
281	C₂×D₃	—	18	24	no	—
282	C₂×D₃	—	18	64	no	—
283	C₂×D₃	—	36	96	no	—
284	C₂×D₃	C₂×C₄⋊(C₃⋊D₃)	1	24	yes	direct product factor
285	C₂×D₃	C₂³×C₃⋊D₃	1	4	yes	—
286	C₃×C₄	—	2	16	no	—
287	C₃×C₄	—	3	16	no	—
288	C₃×C₄	C₂²×D₃²	1	16	yes	complemented
289	C₃×C₄	C₂³×C₃⋊D₃	1	4	yes	complemented
290	Dic₃	C₂³×C₃⋊D₃	1	4	yes	complemented
291	C₃²	—	2	4	no	—
292	C₃²	C₂³×D₁₂	1	4	yes	complemented
293	C₃²	C₂²×D₃×D₄	1	1	yes	characteristic, complemented
294	C₂³	—	3	6	no	—
295	C₂³	—	3	8	no	—
296	C₂³	—	9	12	no	—
297	C₂³	—	18	8	no	—
298	C₂³	—	27	32	no	—
299	C₂³	—	27	12	no	—
300	C₂³	—	54	96	no	—
301	C₂³	—	54	8	no	—
302	C₂³	C₂×D₃×C₃⋊D₃	1	1	yes	characteristic
303	D₄	—	9	16	no	—
304	D₄	—	27	32	no	—
305	D₄	—	27	16	no	—
306	C₂×C₄	—	3	6	no	—
307	C₂×C₄	—	3	16	no	—
308	C₂×C₄	C₂×D₃×C₃⋊D₃	1	6	yes	complemented
309	C₂×C₃	—	2	24	no	—
310	C₂×C₃	—	2	4	no	—
311	C₂×C₃	—	3	32	no	—
312	C₂×C₃	—	18	8	no	—
313	C₂×C₃	C₂×D₃×D₁₂	1	24	yes	complemented
314	C₂×C₃	C₂²×C₄⋊(C₃⋊D₃)	1	6	yes	complemented
315	C₂×C₃	C₂³×D₃²	1	4	yes	—
316	C₂×C₃	C₂⁴×C₃⋊D₃	1	1	yes	characteristic
317	D₃	—	6	32	no	—
318	D₃	—	18	32	no	—
319	D₃	—	18	8	no	—
320	D₃	—	36	32	no	—
321	D₃	C₂²×C₄⋊(C₃⋊D₃)	1	8	yes	direct product factor
322	C₂²	—	3	24	no	—
323	C₂²	—	3	4	no	—
324	C₂²	—	9	8	no	—
325	C₂²	—	18	24	no	—
326	C₂²	—	27	8	no	—
327	C₂²	—	54	64	no	—
328	C₂²	—	54	24	no	—
329	C₂²	D₃×C₄⋊(C₃⋊D₃)	1	4	yes	direct product factor
330	C₂²	C₂²×D₃×C₃⋊D₃	1	3	yes	—
331	C₄	—	3	4	no	—
332	C₄	C₂²×D₃×C₃⋊D₃	1	4	yes	complemented
333	C₃	—	2	4	no	—
334	C₃	C₂²×D₃×D₁₂	1	4	yes	complemented
335	C₃	C₂³×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented
336	C₂	—	3	8	no	—
337	C₂	—	18	8	no	—
338	C₂	—	54	8	no	—
339	C₂	C₂×D₃×C₄⋊(C₃⋊D₃)	1	6	yes	direct product factor
340	C₂	C₂³×D₃×C₃⋊D₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₃×C₃⋊D₃
commutator, cosocle	C₂×C₃³	C₂⁵
Frattini	C₂	C₂³×D₃×C₃⋊D₃
Fitting	C₂²×C₃³×C₄	C₂²
socle	C₂³×C₃³	C₂³
hypercenter	C₂²×C₄	D₃×C₃⋊D₃
hypocenter	C₃³	C₂³×D₄
LCS	G ▷ C₂×C₃³ ▷ C₃³
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂³×D₃×C₃⋊D₃	C₂	semidirect
2. C₂²×C₄⋊(C₃⋊(C₃⋊D₃))	C₂	semidirect
3. C₂²×C₃×C₄⋊(C₃⋊D₃)	C₂	semidirect
4. C₂²×C₃²×C₄×D₃	C₂	semidirect
5. C₂²×#6292	C₂	semidirect
6. C₂×D₃×C₄⋊(C₃⋊D₃)	C₂	direct (N × H)
9. C₂³×C₃⋊(C₃⋊D₃)	C₂²	semidirect
10. C₂³×C₃×C₃⋊D₃	C₂²	semidirect
13. C₂²×D₃×C₃⋊D₃	C₂²	semidirect
14. C₂²×C₃³×C₄	C₂²	semidirect
15. C₂×C₄⋊(C₃⋊(C₃⋊D₃))	C₂²	semidirect
16. C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	semidirect
17. C₂²×C₃²×Dic₃	C₂²	semidirect
18. C₂×C₃²×C₄×D₃	C₂²	semidirect
19. C₂×#6292	C₂²	semidirect
20. D₃×C₄⋊(C₃⋊D₃)	C₂²	direct (N × H)
29. C₂²×C₄⋊(C₃⋊D₃)	D₃	direct (N × H)
31. C₂²×C₃×C₄×D₃	D₃	semidirect
36. C₂²×C₃⋊(C₃⋊D₃)	C₂³	semidirect
38. C₂²×C₃×C₃⋊D₃	C₂³	semidirect
39. C₂²×C₃²×D₃	D₄	semidirect
42. C₂×D₃×C₃⋊D₃	C₂³	semidirect
43. C₂×C₃³×C₄	C₂³	semidirect
44. C₄⋊(C₃⋊(C₃⋊D₃))	C₂³	semidirect
45. C₃×C₄⋊(C₃⋊D₃)	C₂³	semidirect
46. C₂×C₃²×Dic₃	C₂³	semidirect
47. C₃²×C₄×D₃	C₂³	semidirect
48. #6292	C₂³	semidirect
57. C₂³×C₃⋊D₃	C₂×D₃	semidirect
65. C₂²×C₃²×C₄	C₂×D₃	semidirect
66. C₂²×C₃²×C₄	C₂×D₃	semidirect
72. C₂×C₄⋊(C₃⋊D₃)	C₂×D₃	direct (N × H)
73. C₂²×C₃×Dic₃	C₂×D₃	semidirect
75. C₂×C₃×C₄×D₃	C₂×D₃	semidirect
78. C₂²×C₃³	C₂×D₄	semidirect
81. C₂×C₃⋊(C₃⋊D₃)	C₂⁴	semidirect
83. C₂×C₃×C₃⋊D₃	C₂⁴	semidirect
84. C₂×C₃²×D₃	C₂×D₄	semidirect
87. C₃³×C₄	C₂⁴	semidirect
88. C₃²×Dic₃	C₂⁴	semidirect
101. C₂²×C₄×D₃	C₃⋊D₃	semidirect
116. C₂²×C₃⋊D₃	C₂²×D₃	semidirect
119. C₂²×C₃×D₃	D₁₂	semidirect
126. C₂×C₃²×C₄	C₂²×D₃	semidirect
127. C₂×C₃²×C₄	C₂²×D₃	semidirect
132. C₄⋊(C₃⋊D₃)	C₂²×D₃	direct (N × H)
133. C₂×C₃×Dic₃	C₂²×D₃	semidirect
135. C₃×C₄×D₃	C₂²×D₃	semidirect
138. C₂×C₃³	C₂²×D₄	semidirect
142. C₃²×D₃	C₂²×D₄	semidirect
158. C₂²×C₃×C₄	D₃²	semidirect
159. C₂²×C₃×C₄	C₂×C₃⋊D₃	semidirect
161. C₂²×Dic₃	C₂×C₃⋊D₃	semidirect
169. C₂×C₄×D₃	C₂×C₃⋊D₃	semidirect
174. C₂²×C₃²	C₂×D₁₂	semidirect
175. C₂²×C₃²	D₃×D₄	semidirect
186. C₂×C₃⋊D₃	C₂³×D₃	semidirect
189. C₂×C₃×D₃	C₂×D₁₂	semidirect
194. C₃²×C₄	C₂³×D₃	semidirect
195. C₃²×C₄	C₂³×D₃	semidirect
196. C₃×Dic₃	C₂³×D₃	semidirect
203. C₃³	C₂³×D₄	semidirect
223. C₂²×D₃	C₄⋊(C₃⋊D₃)	direct (N × H)
229. C₂×C₃×C₄	C₂×D₃²	semidirect
230. C₂×C₃×C₄	C₂²×C₃⋊D₃	semidirect
232. C₂×Dic₃	C₂²×C₃⋊D₃	semidirect
238. C₄×D₃	C₂²×C₃⋊D₃	semidirect
242. C₂×C₃²	C₂²×D₁₂	semidirect
243. C₂×C₃²	C₂×D₃×D₄	semidirect
251. C₃×D₃	C₂²×D₁₂	semidirect
263. C₂²×C₄	D₃×C₃⋊D₃	semidirect
270. C₂²×C₃	D₃×D₁₂	semidirect
271. C₂²×C₃	C₂×C₄⋊(C₃⋊D₃)	semidirect
284. C₂×D₃	C₂×C₄⋊(C₃⋊D₃)	direct (N × H)
288. C₃×C₄	C₂²×D₃²	semidirect
289. C₃×C₄	C₂³×C₃⋊D₃	semidirect
290. Dic₃	C₂³×C₃⋊D₃	semidirect
292. C₃²	C₂³×D₁₂	semidirect
293. C₃²	C₂²×D₃×D₄	semidirect
308. C₂×C₄	C₂×D₃×C₃⋊D₃	semidirect
313. C₂×C₃	C₂×D₃×D₁₂	semidirect
314. C₂×C₃	C₂²×C₄⋊(C₃⋊D₃)	semidirect
321. D₃	C₂²×C₄⋊(C₃⋊D₃)	direct (N × H)
329. C₂²	D₃×C₄⋊(C₃⋊D₃)	direct (N × H)
332. C₄	C₂²×D₃×C₃⋊D₃	semidirect
334. C₃	C₂²×D₃×D₁₂	semidirect
335. C₃	C₂³×C₄⋊(C₃⋊D₃)	semidirect
339. C₂	C₂×D₃×C₄⋊(C₃⋊D₃)	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂³×D₃×C₃⋊D₃	2
C₂²×C₄⋊(C₃⋊(C₃⋊D₃))	2
C₂²×C₃×C₄⋊(C₃⋊D₃)	2
C₂²×C₃²×C₄×D₃	2
C₂²×#6292	2
C₂×D₃×C₄⋊(C₃⋊D₃)	2
C₂³×C₄⋊(C₃⋊D₃)	3
C₂²×D₃×D₁₂	3

Subgroups — C22×D3×C4⋊(C3⋊D3) #13181599

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×D₃×C₄⋊(C₃⋊D₃) #13181599